Heat is lost from a body or any LIQUID by three means
Conduction, radiation and evaporation.
Radiation is not affected by the movement of air.
Air, however, is a very poor conductor of heat, this is why "Foam cell" insulation works so well. But it can absorb a bit of heat, so if we move more fresh cold air in to replace the now hot air, it an absorbe a bit more heat. So yes, moving air does cool even a block of steel faster than air that is not moving.
And evaporation.. As the air close to the hot liquid or body becomes saturated with moisture (The evaporation of which takes great hugh gobs of heat from the body, or the hot bowl of soup) fresh dry air comes in to replace it and evaporation continues.
By the way this is the real reason you blow on your soup.